广义Pareto分布变点检测重现期预测模型及其应用  

Generalized Pareto distribution change point detection model and its application in modeling return period prediction

作　　者：胡尧 谌业文[2] 王旭琴 刘伟 HU Yao;CHEN Yewen;WANG Xuqin;LIU Wei(School of Mathematics and Statistics,Guizhou University,Guiyang 550025,China;School of Mathematics,Sun Yat-sen University,Guangzhou 510000,China;The School of Economics,Xiamen University,Xiamen 361005,China;Guizhou Provincial Key Laboratory of Public Big Data,Guizhou University,Guiyang 550025,China)

机构地区：[1]贵州大学数学与统计学院,贵阳550025 [2]中山大学数学学院,广州510000 [3]厦门大学经济学院,厦门361005 [4]贵州大学贵州省公共大数据重点实验室,贵阳550025

出　　处：《系统工程理论与实践》2021年第9期2379-2391,共13页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(12161016,11661018);贵州省科技计划项目(黔科合平台人才[2017]5788号);贵州省数据驱动建模学习与优化创新团队(黔科合平台人才[2020]5016);全国统计科学研究项目(2014LZ46)。

摘　　要：广义Pareto分布(generalized Pareto distribution,GPD)变点是指其超出量发生质变的点,具体表现为一个或多个参数的变化.本文将极端暴雨数据的三参数GPD变点检测问题表示为假设检验问题,通过极大似然比检验统计量解决.尽管不可能得到检验统计量的精确分布,但通过证明GPD变点的极限性质和检验统计量的渐近收敛定理,可得到它的极限分布.同时,利用GPD变点检测模型,对深圳55年的月最大暴雨数据进行了分析.结果发现20世纪80年代是深圳气象学的一个变点,这与最小超阈值(narrowest over threshold,NOT)方法所得结果一致.除此之外,本文方法的优势在于它统一了变点检测前后的分析框架.在此框架下,通过对变点的分析,发现GPD变点之前的极值指数为负.结合降雨量与重现期的关系可得,重现期小于百年的暴雨强度较之前有所减弱.该点之后,极值指数为正,百年以上重现期的暴雨灾害程度较之前严重且极端降雨现象较之前频繁.实证结果表明,GPD变点模型能够较好地捕获传统GPD模型所不能捕捉的内在规律,较好地弥补了传统GPD模型的不足.Generalized Pareto distribution(GPD) change point refers to the point where the quantity whose the peak over threshold changes qualitatively,which shows the change of one or more GPD paramethers.In this paper,the detection issue of GPD change point with three parameters for extreme rainstorm data was expressed as the hypothesis test problem which could be solved by the maximum likelihood ratio test statistic.Although it is impossible to derive an exact distribution of this test statistic,fortunately,we obtained its limiting distribution by proving the limit properties of the GPD change point and the asymptotic convergence theorem of the test statistic.Meanwhile,the detection model we developed was used to analyze the monthly maximum precipitation data of Shenzhen with a total number of 55 years.As a result,we found the 1980 s is a change point of Shenzhen meteorology,which is identical with the narrowest over threshold(NOT) method.In addition,the advantage of GPD change point method is that it ensures a consistent analytical framework before and after the detection of change point.In this framework,the analysis of GPD change point revealed that the extreme value index before that point is negative.Combining the relationship between rainfall and the return period,it might be concluded that the severity of rainstorm in the return period less than 100 years is weaker than before.After that point,the extreme value index is positive,and the degree of rainstorm disaster in the return period more than100 years is more serious and the phenomenon of extreme rainstorm is more frequent than before.The empirical result showed that the GPD change point model is capable to capture the potential rules that the conventional GPD model impotently,which could moderately make up for the deficiency of conventional GPD model in this respect.

关 键 词：广义Pareto分布(GPD)变点 似然比检验统计量 变点检测 重现期 最小超阈值(NOT)方法 预测模型 

分 类 号：O212.1[理学—概率论与数理统计] P333.6[理学—数学]